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A simple additivity test for conditionally heteroscedastic nonlinear autoregression


  • Levine, Michael
  • Li, Jinguang (Tony)


In this article, we propose a test for the additivity of a nonlinear conditionally heteroscedastic autoregressive model. The test is based on the unequal variance unbalanced design ANOVA scheme. An asymptotic distribution of the test statistic is derived and the test performance in finite samples is studied using simulation. To the best of our knowledge, this is the first additivity test for a conditionally heteroscedastic time series model.

Suggested Citation

  • Levine, Michael & Li, Jinguang (Tony), 2012. "A simple additivity test for conditionally heteroscedastic nonlinear autoregression," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2421-2429.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:8:p:2421-2429 DOI: 10.1016/j.csda.2012.01.019

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    References listed on IDEAS

    1. K. S. Chan, 2003. "Bürmann expansion and test for additivity," Biometrika, Biometrika Trust, vol. 90(1), pages 209-222, March.
    2. Markku Lanne & Pentti Saikkonen, 2005. "Non-linear GARCH models for highly persistent volatility," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 251-276, July.
    3. Li, C W & Li, W K, 1996. "On a Double-Threshold Autoregressive Heteroscedastic Time Series Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 253-274, May-June.
    4. Hwang, S. Y. & Woo, Mi-Ja, 2001. "Threshold ARCH(1) processes: asymptotic inference," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 11-20, May.
    5. Sperlich, Stefan & Tj stheim, Dag & Yang, Lijian, 2002. "Nonparametric Estimation And Testing Of Interaction In Additive Models," Econometric Theory, Cambridge University Press, vol. 18(02), pages 197-251, April.
    6. Lu, Zudi & Jiang, Zhenyu, 2001. "L1 geometric ergodicity of a multivariate nonlinear AR model with an ARCH term," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 121-130, January.
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